A message signal $m (t) = 5 s i n c (500 t) V$ is applied to a frequency modulator whose carrier frequency is $100 M H z$ and frequency sensitivity is $400 H z / V$ . The modulation index (or the deviation ratio) of the resultant $F M$ signal will be
$[$ Assume that, $s i n c (t) = s i n (π t) / π t]$

8

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Solution

The correct option is A $8$
$m (t) = 5 s i n c (500 t) V$
$M (f) = \frac{5}{500} r e c t (\frac{f}{500})$
$| m (t) |_{m a x} = 5 V$
$f_{m (m a x)} = \frac{500}{2} = 250 H z$
The modulation index of an $F M$ signal can be given by,
$β = \frac{k_{f} | m (t) |_{m a x}}{f_{m (m a x)}} = \frac{400 \times 5}{250} = 8$

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A message signal m(t)=5 sin c(500 t) V is applied to a frequency modulator whose carrier frequency is 100 MHz and frequency sensitivity is 400 Hz/V. The modulation index (or the deviation ratio) of the resultant FM signal will be [ Assume that, sin c(t)=sin(πt)/πt]

The correct option is A 8m(t)=5sin c(500t) V M(f)=5500rect(f500) |m(t)|max=5 V fm(max)=5002=250 Hz The modulation index of an FM signal can be given by, β=kf|m(t)|maxfm(max)=400×5250=8